Preventing interference between tooth models

ABSTRACT

Systems and methods are disclosed to prevent interference between two physical tooth models in a physical dental arch model by acquiring the coordinates of a plurality of points on the surfaces of each of the two physical tooth models and digitally representing the surfaces of each of the two physical tooth models by a mesh of points in three dimensions using the acquired coordinates. The meshes representing the surfaces of the two physical tooth models intersect at least at one point to form an overlapping portion. The method also includes calculating the depth of the overlapping portion between the two meshes to quantify the interference of the two physical tooth models.

CROSS-REFERENCES TO RELATED INVENTIONS

This application is a continuation of U.S. patent application Ser. No.16/697,072, filed Nov. 26, 2019, which is a continuation of U.S. patentapplication Ser. No. 15/907,106, filed Feb. 27, 2018, now U.S. Pat. No.10,524,880, which is a continuation of U.S. patent application Ser. No.15/369,145, filed Dec. 5, 2016, now U.S. Pat. No. 9,943,382, which is acontinuation of U.S. patent application Ser. No. 14/641,926, filed Mar.9, 2015, now U.S. Pat. No. 9,536,020, which is a continuation of U.S.patent application Ser. No. 13/241,090, filed Sep. 22, 2011, now U.S.Pat. No. 9,011,149, which is a continuation of U.S. patent applicationSer. No. 11/933,350, filed Oct. 31, 2007, now U.S. Pat. No. 8,047,846,which is a continuation of U.S. patent application Ser. No. 11/013,154,filed Dec. 14, 2004, now U.S. Pat. No. 7,309,230, the entire contents ofeach are herein incorporated by reference.

The present invention is also related to commonly assigned U.S. patentapplication Ser. No. 11/013,152, now U.S. Pat. No. 7,922,490, titled“Base for physical dental arch model” by Huafeng Wen, filed Dec. 14,2004, commonly assigned U.S. patent application Ser. No. 11/012,924,titled “Accurately producing a base for physical dental arch model” byHuafeng Wen, filed Dec. 14, 2004, commonly assigned U.S. patentapplication Ser. No. 11/013,145, now U.S. Pat. No. 8,636,513, titled“Fabricating a base compatible with physical dental tooth models” byHuafeng Wen, filed Dec. 14, 2004, commonly assigned U.S. patentapplication Ser. No. 11/013,156, titled “Producing non-interfering toothmodels on a base” by Huafeng Wen, filed Dec. 14, 2004, commonly assignedU.S. patent application Ser. No. 11/013,160, now U.S. Pat. No.7,435,084, titled “System and methods for casting physical tooth model”by Huafeng Wen, filed Dec. 14, 2004, commonly assigned U.S. patentapplication Ser. No. 11/013,159, titled “Producing a base for accuratelyreceiving dental tooth models” by Huafeng Wen, and filed Dec. 14, 2004,commonly assigned U.S. patent application Ser. No. 11/013,157, titled“Producing accurate base for dental arch model” by Huafeng Wen, filedDec. 14, 2004.

The present invention is also related to U.S. patent application Ser.No. 10/979,823, now U.S. Pat. No. 7,384,266, titled “Method andapparatus for manufacturing and constructing a physical dental archmodel” by Huafeng Wen, filed Nov. 2, 2004, now U.S. Pat. No. 7,384,266,issued Jun. 10, 2008, U.S. patent application Ser. No. 10/979,497,titled “Method and apparatus for manufacturing and constructing a dentalaligner” by Huafeng Wen, 11/02/2004, U.S. patent application Ser. No.10/979,504, titled “Producing an adjustable physical dental arch model”by Huafeng Wen, filed Nov. 2, 2004, and U.S. patent application Ser. No.10/979,824, titled “Producing a base for physical dental arch model” byHuafeng Wen, 11/02/2004. The disclosures of these related applicationsare incorporated herein by reference.

TECHNICAL FIELD

This application generally relates to the field of dental care, and moreparticularly to a system and a method for manufacturing and constructingphysical tooth models.

BACKGROUND

Orthodontics is the practice of manipulating a patient's teeth toprovide better function and appearance. In treatments using fixedappliance, brackets are bonded to a patient's teeth and coupled togetherwith an arched wire. The combination of the brackets and wire provide aforce on the teeth causing them to move. Once the teeth have moved to adesired location and are held in a place for a certain period of time,the body adapts bone and tissue to maintain the teeth in the desiredlocation. To further assist in retaining the teeth in the desiredlocation, a patient may be fitted with a retainer.

To achieve tooth movement, orthodontists and dentists typically reviewpatient data such as X-rays and models such as impressions of teeth.They can then determine a desired orthodontic goal for the patient. Withthe goal in mind, the orthodontists place the brackets and/or bands onthe teeth and manually bend (i.e., shape) wire, such that a force isasserted on the teeth to reposition the teeth into the desiredpositions. As the teeth move towards the desired position, theorthodontist makes continual adjustments based on the progress of thetreatment.

U.S. Pat. No. 5,518,397 issued to Andreiko, et. al. provides a method offorming an orthodontic brace. Such a method includes obtaining a modelof the teeth of a patient's mouth and a prescription of desiredpositioning of such teeth. The contour of the teeth of the patient'smouth is determined, from the model. Calculations of the contour and thedesired positioning of the patient's teeth are then made to determinethe geometry (e.g., grooves or slots) to be provided. Custom bracketsincluding a special geometry are then created for receiving an arch wireto form an orthodontic brace system. Such geometry is intended toprovide for the disposition of the arched wire on the bracket in aprogressive curvature in a horizontal plane and a substantially linearconfiguration in a vertical plane. The geometry of the brackets isaltered, (e.g., by cutting grooves into the brackets at individualpositions and angles and with particular depth) in accordance with suchcalculations of the bracket geometry. In such a system, the brackets arecustomized to provide three-dimensional movement of the teeth, once thewire, which has a two-dimensional shape (i.e., linear shape in thevertical plane and curvature in the horizontal plane), is applied to thebrackets.

Other innovations relating to bracket and bracket placements have alsobeen patented. For example, such patent innovations are disclosed inU.S. Pat. No. 5,618,716 entitled “Orthodontic Bracket and Ligature” amethod of ligating arch wires to brackets, U.S. Pat. No. 5,011,405“Entitled Method for Determining Orthodontic Bracket Placement,” U.S.Pat. No. 5,395,238 entitled “Method of Forming Orthodontic Brace,” andU.S. Pat. No. 5,533,895 entitled “Orthodontic Appliance and GroupStandardize Brackets therefore and methods of making, assembling andusing appliance to straighten teeth”.

Kuroda et al. (1996) Am. J. Orthodontics 110:365-369 describes a methodfor laser scanning a plaster dental cast to produce a digital image ofthe cast. See also U.S. Pat. No. 5,605,459. U.S. Pat. Nos. 5,533,895;5,474,448; 5,454,717; 5,447,432; 5,431,562; 5,395,238; 5,368,478; and5,139,419, assigned to Ormco Corporation, describe methods formanipulating digital images of teeth for designing orthodonticappliances.

U.S. Pat. No. 5,011,405 describes a method for digitally imaging a toothand determining optimum bracket positioning for orthodontic treatment.Laser scanning of a molded tooth to produce a three-dimensional model isdescribed in U.S. Pat. No. 5,338,198. U.S. Pat. No. 5,452,219 describesa method for laser scanning a tooth model and milling a tooth mold.Digital computer manipulation of tooth contours is described in U.S.Pat. Nos. 5,607,305 and 5,587,912. Computerized digital imaging of thearch is described in U.S. Pat. Nos. 5,342,202 and 5,340,309.

Other patents of interest include U.S. Pat. Nos. 5,549,476; 5,382,164;5,273,429; 4,936,862; 3,860,803; 3,660,900; 5,645,421; 5,055,039;4,798,534; 4,856,991; 5,035,613; 5,059,118; 5,186,623; and 4,755,139.

U.S. Pat. No. 5,431,562 to Andreiko et al. describes a computerized,appliance-driven approach to orthodontics. In this method, first certainshape information of teeth is acquired. A uniplanar target arcform iscalculated from the shape information. The shape of customized bracketslots, the bracket base, and the shape of the orthodontic archwire, arecalculated in accordance with a mathematically-derived target archform.The goal of the Andreiko et al. method is to give more predictability,standardization, and certainty to orthodontics by replacing the humanelement in orthodontic appliance design with a deterministic,mathematical computation of a target arch form and appliance design.Hence the '562 patent teaches away from an interactive, computer-basedsystem in which the orthodontist remains fully involved in patientdiagnosis, appliance design, and treatment planning and monitoring.

More recently, removable appliances from companies such as AlignTechnology, Inc. began offering transparent, removable aligning devicesas a new treatment modality in orthodontics. In this system, animpression model of the dentition of the patient is obtained by theorthodontist and shipped to a remote appliance manufacturing center,where it is scanned with a CT scanner. A computer model of the dentitionin a target situation is generated at the appliance manufacturing centerand made available for viewing to the orthodontist over the Internet.The orthodontist indicates changes they wish to make to individual toothpositions. Later, another virtual model is provided over the Internet,and the orthodontist reviews the revised model and indicates any furtherchanges. After several such iterations, the target situation is agreedupon. A series of removable aligning devices or shells are manufacturedand delivered to the orthodontist. The shells, in theory, will move thepatient's teeth to the desired or target position.

The practice of orthodontics and other dental treatments includingpreparation of a denture can benefit from a physical dental arch modelthat is representative of the dentition and the alveolar ridge of apatient to be orthodontically treated. The physical dental arch model,also referred as a physical dental arch model, is often prepared basedon an impression model. The physical dental arch model is generallyprepared by cutting and arranging individual teeth on the alveolar ridgeof the impression model. With this physical dental arch model soprepared, not only is a final goal for the dental treatment made clear,but also the occlusal condition between the maxillary and the mandibulardentitions can be specifically ascertained.

Also, the patient when the physical dental arch model is presented canvisually ascertain the possible final result of orthodontic treatment heor she will receive and, therefore, the physical dental arch model is aconvenient presentation tool to the patient.

Making a model for a whole or a large portion of an arch is moredifficult than making one tooth abutment for implant purposes. Singletooth does not have the concavities and complexities as in theinter-proximal areas of teeth in an arch. Some prior art making thephysical dental arch model is carried out manually, involving not only asubstantial amount of labor required, but also a substantial amount oftime. It is also difficult to machine an accurate arch model because ofthe various complex shapes and the complex features such asinter-proximal areas, wedges between teeth, among others, in an arch.

Another issue with the assembling of tooth models into a physical dentalarch model is that the adjacent tooth models can sometimes interferewith each other during an orthodontic treatment. The interference canoccur between the tooth portions of the two neighboring tooth modelswhen they are inserted into a base plate, or between the pins thatassist them to be mounted onto a base plate.

SUMMARY OF THE INVENTION

Systems and methods provide a practical, effective and efficient methodsand apparatus to manufacture and construct the physical dental archmodel.

In one aspect, the present invention relates to a method for preventinginterference between two physical tooth models in a physical dental archmodel, comprising:

-   -   acquiring the coordinates of a plurality of points on the        surfaces of each of the two physical tooth models;    -   digitally representing the surfaces of each of the two physical        tooth models by a mesh of points in three dimensions using the        acquired coordinates, wherein the meshes representing the        surfaces of the two physical tooth models intersect at least at        one point to form an overlapping portion; and    -   calculating the depth of the overlapping portion between the two        meshes to quantify the interference of the two physical tooth        models.

In another aspect, the present invention relates to a method forpreventing interference between two physical tooth models in a physicaldental arch model, comprising:

-   -   acquiring the coordinates of a plurality of points on the        surfaces of each of the two physical tooth models;    -   digitally representing the surfaces of each of the two physical        tooth models by a mesh of points in three dimensions using the        acquired coordinates, wherein the meshes representing the        surfaces of the two physical tooth models intersect at least at        one point to form an overlapping portion;    -   calculating the depth of the overlapping portion between the two        meshes; and    -   adjusting the positions or the orientations of at least one of        the two physical tooth models in accordance with the depth of        the overlapping portion between the two physical tooth models to        prevent the interference between the physical tooth models.

In yet another aspect, the present invention relates to a method forpreventing interference between two physical tooth models in a physicaldental arch model, comprising:

-   -   acquiring the coordinates of a plurality of points on the        surfaces of each of the two physical tooth models;    -   digitally representing the surfaces of each of the two physical        tooth models by a mesh of points in three dimensions using the        acquired coordinates;    -   interpolating each of the two meshes to produce one or more        surfaces to represent the boundaries of one of the two physical        tooth models, wherein the interpolated surfaces intersect at        least at one point to form an overlapping portion; and    -   calculating the depth of the overlapping portion between the two        interpolated surfaces to quantify the interference of the two        physical tooth models.

Embodiments may include one or more of the following advantages. Anadvantage of the present invention is that adjacent physical toothmodels in a physical dental arch model can be simulated. Theinterference between the two physical models can be predicted beforethey are assembled to form a physical arch model. The positions and theorientations of the tooth models can be adjusted to prevent theinterference. As a result, the precision and effectiveness of theorthodontic treatments are improved.

Another advantage of the present invention is that the physical toothmodels can be used to form different tooth arch models having differentteeth configurations. The pin configurations can be modified withoutchanging the tooth models themselves to be modified to preventinterference between adjacent tooth models at different steps of anorthodontic treatment. Moreover, the tooth models can be reused as toothpositions are changed during a treatment process. Much of the cost ofmaking multiple tooth arch models in orthodontic treatment are thereforeeliminated. The tooth models can have pins that assist their assemblingwith a base.

Another advantage of the present invention is that the same base cansupport different tooth arch models having different teethconfigurations. The base can include more than one sets of receivingfeatures that can receive tooth models at different positions. Thereusable base further reduces cost in the dental treatment of teethalignment. Furthermore, the receiving features can be modified toreceive tooth models having different pin configurations to avoidinterference between the adjacent tooth models in a tooth arch model.

The physical tooth models include features to allow them to be attached,plugged or locked to a base. The physical tooth models can beprefabricated having standard registration and attaching features forassembling. The physical tooth models can be automatically assembledonto a base by a robotic arm under computer control.

The physical dental arch model obtained by the disclosed system andmethods can be used for various dental applications such as dentalcrown, dental bridge, aligner fabrication, biometrics, and teethwhitening. The arch model can be assembled from segmented manufacturablecomponents that can be individually manufactured by automated, precisenumerical manufacturing techniques.

The physical tooth models in the physical dental arch model can beeasily separated, repaired or replaced, and reassembled after theassembly without the replacement of the whole arch model. Themanufacturable components can be attached to a base. The assembledphysical dental arch model specifically corresponds to the patient'sarch. There is no need for complex and costly mechanisms such asmicro-actuators for adjusting multiple degrees of freedom for each toothmodel. The described methods and system is simple to make and easy touse.

The details of one or more embodiments are set forth in the accompanyingdrawing and in the description below. Other features, objects, andadvantages of the invention will become apparent from the descriptionand drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawing, which are incorporated in and form a part ofthis specification, illustrate embodiments of the invention and,together with the description, serve to explain the principles of theinvention:

FIG. 1 is a flow chart for producing a physical dental arch model inaccordance with the present invention.

FIG. 2 illustrates a tooth model and a base respectively comprisingcomplimentary features for assembling the tooth model with the base.

FIG. 3 illustrates fixing a stud to a tooth model comprising a femalesocket to produce a tooth model having a protruded stud.

FIG. 4 illustrate a tooth model comprising two pins that allow the toothmodel to be plugged into two corresponding holes in a base.

FIG. 5 illustrate a tooth model comprising a protruded pin that allowsthe tooth model to be plugged into a hole in a base.

FIG. 6 illustrates cone shaped studs protruded out of the bottom of atooth model.

FIG. 7 illustrates exemplified shapes for the studs at the bottom of atooth model.

FIG. 8A illustrates an example of a base comprising a plurality offemale sockets for receiving a plurality of tooth models for forming aphysical dental arch model.

FIG. 8B illustrates another example of a base comprising a plurality offemale sockets for receiving a plurality of tooth models for forming aphysical dental arch model.

FIG. 9 illustrates a tooth model that can be assembled to the base inFIGS. 8A and 8B.

FIG. 10 illustrates an example in which the pins at the bottom portionsof two adjacent tooth models interfere with each other.

FIG. 11 illustrates an example in which two adjacent tooth modelsmounted on a base interfere with each other at the tooth portions of thetooth models.

FIG. 12 illustrates a tooth model having pin configurations that preventthe tooth models from interfering with each other.

FIG. 13(a) is a front view of two tooth models having pin configurationsof FIG. 12 .

FIG. 13(b) is a perspective bottom view of two tooth models having pinconfigurations of FIG. 12 .

FIG. 14 illustrates a mechanism for fixing tooth models to a base usingremovable pins.

FIG. 15 illustrates a mechanism for fixing tooth models to a base usingspring-loaded pins to prevent interference between tooth models.

FIG. 16 illustrates a triangulated mesh that simulates the surfaces of apatient's tooth.

FIG. 17 illustrates the calculation of the buffer width.

FIG. 18 illustrates the set-up of an orthogonal bounding box forcalculating the buffer width.

FIG. 19 shows the grid over a rectangular face of a bounding box for thedigital tooth model.

FIG. 20 illustrates the calculation of the interference depth betweentwo tooth models.

DESCRIPTION OF THE INVENTION

Major operations in producing a physical dental arch model areillustrated in FIG. 1 . The process generally includes the followingsteps. First individual tooth model is created in step 110. Anindividual tooth model is a physical model that can be part of aphysical tooth arch model, which can be used in various dentalapplications. Registration features are next added to the individualtooth model to allow them to be attached to each other or a base in step120. A base is designed for receiving the tooth model in step 130. Thetooth model positions in a tooth arch model are next determined in step140. The digital tooth models are developed in step 150. Theinterference between the physical tooth models is predicted in step 160.In step 170, the pin configurations affixed to the tooth models areselected to prevent interference between adjacent tooth models when theyare mounted on the base. A base is fabricated in step 180. The baseincludes features for receiving the individual tooth model having theselected pin configurations. The tooth models are finally attached tothe base at the predetermined positions using the pre-designed featuresin step 190.

Details of process in FIG. 1 are now described. Individual tooth modelcan be obtained in step 110 in a number of different methods. The toothmodel can be created by casting. A negative impression is first madefrom a patient's arch using for example PVS. A positive of the patient'sarch is next made by pouring a casting material into the negativeimpression. After the material is dried, the mold is then taken out withthe help of the impression knife. A positive of the arch is thusobtained.

In an alternative approach, the negative impression of the patient'sarch is placed in a specially designed container. A casting material isthen poured into the container over the impression to create a model. Alid is subsequently placed over the container. The container is openedand the mold can be removed after the specified time.

Examples of casting materials include auto polymerizing acrylic resin,thermoplastic resin, light-polymerized acrylic resins, polymerizingsilicone, polyether, plaster, epoxies, or a mixture of materials. Thecasting material is selected based on the uses of the cast. The materialshould be easy for cutting to obtain individual tooth model.Additionally, the material needs to be strong enough for the tooth modelto take the pressure in pressure form for producing a dental aligner.Details of making a dental aligner are disclosed in commonly assignedand above referenced US Patent Application titled “Method and apparatusfor manufacturing and constructing a dental aligner” by Huafeng Wen,filed Nov. 2, 2004, the content of which is incorporated herein byreference.

Features that can allow tooth models to be attached to a base (step 120)can be added to the casting material in the casting process.Registration points or pins can be added to each tooth before thecasting material is dried. Optionally, universal joints can be insertedat the top of the casting chamber using specially designed lids, whichwould hang the universal joints directly into the casting area for eachtooth.

Still in step 110, individual tooth models are next cut from the archpositive. One requirement for cutting is to obtain individual teeth insuch a manner that they can be joined again to form a tooth arch. Theseparation of individual teeth from the mold can be achieved using anumber of different cutting methods including laser cutting andmechanical sawing.

Separating the positive mold of the arch into tooth models may result inthe loss of the relative 3D coordinates of the individual tooth modelsin an arch. Several methods are provided in step 120 for findingrelative position of the tooth models. In one embodiment, uniqueregistration features are added to each pair of tooth models before thepositive arch mold is separated. The separated tooth models can beassembled to form a physical dental arch model by matching tooth modelshaving the same unique registration marks.

The positive arch mold can also be digitized by a three-dimensionalscanning using a technique such as laser scanning, optical scanning,destructive scanning, CT scanning and Sound Wave Scanning. A digitaldental arch model is therefore obtained. The digital dental arch modelis subsequently smoothened and segmented. Each segment can be physicallyfabricated by CNC based manufacturing to obtain individual tooth models.The digital dental arch model tracks and stores the positions of theindividual tooth models. Unique registration marks can be added to thedigital tooth models that can be made into a physical feature in CNCbase manufacturing.

Examples of CNC based manufacturing include CNC based milling,Stereolithography, Laminated Object Manufacturing, Selective LaserSintering, Fused Deposition Modeling, Solid Ground Curing, 3D ink jetprinting. Details of fabricating tooth models are disclosed in commonlyassigned and above referenced US Patent Application titled “Method andapparatus for manufacturing and constructing a physical dental archmode” by Huafeng Wen, filed Nov. 2, 2004, the content of which isincorporated herein by reference.

In another embodiment, the separated tooth models are assembled bygeometry matching. The intact positive arch impression is first scannedto obtain a 3D digital dental arch model. Individual teeth are thenscanned to obtain digital tooth models for individual teeth. The digitaltooth models can be matched using rigid body transformations to match adigital dental arch model. Due to complex shape of the arch,inter-proximal areas, root of the teeth and gingival areas may beignored in the geometry match. High precision is required for matchingfeatures such as cusps, points, crevasses, the front and back faces ofthe teeth. Each tooth is sequentially matched to result in rigid bodytransformations corresponding to the tooth positions that canreconstruct an arch.

In another embodiment, the separated tooth models are assembled andregistered with the assistance of a 3D point picking devices. Thecoordinates of the tooth models are picked up by 3D point pickingdevices such as stylus or Microscribe devices before separation. Uniqueregistration marks can be added on each tooth model in an arch beforeseparation. The tooth models and the registration marks can be labeledby unique IDs. The tooth arch can later be assembled by identifyingtooth models having the same registration marks as were picked from theJaw. 3D point picking devices can be used to pick the same points againfor each tooth model to confirm the tooth coordinates.

The base is designed in step 130 to receive the tooth models. The baseand tooth models include complimentary features to allow them to beassembled together. The tooth model has a protruding structure attachedto it. The features at the base and tooth models can also include aregistration slot, a notch, a protrusion, a hole, an interlockingmechanism, and a jig. The protruding structure can be obtained duringthe casting process or be created after casting by using a CNC machineon each tooth. The positions of the receiving features in the base aredetermined by either the initial positions of the teeth in an arch orthe desired teeth positions during a treatment process (step 140).

The digital tooth models are developed in step 150. First, the surfacesof the two physical tooth models are measured. A negative impression ofa patient's teeth is obtained. A plurality of points on the surfaces ofthe negative impression is measured by a position measurement device.The coordinates of the points in three-dimensional space are obtained.Details of measuring the surface positions of dental impression'ssurfaces are disclosed in the above referenced and commonly assignedU.S. Patent Application, titled “Producing a base for accuratelyreceiving dental tooth models” by Huafeng Wen, and filed 11//2004, andthe above referenced and commonly assigned U.S. Patent Application,titled “Producing accurate base for dental arch model” by Huafeng Wen,filed 11//2004.

The plurality of points representing the surfaces of the negativeimpression is then used to construct a mesh to digitally represent thesurfaces of the patient's teeth in three dimensions. FIG. 16 illustratesa triangulated mesh 1600 that simulates the surfaces of a patient'stooth. The mesh opening can also include other shapes with four, five ormore sides or nodes. The mesh points are interpolated into one or morecontinuous surfaces to represent the surface of the patient's tooth,which serves as a digital model for the tooth.

The interference between two physical tooth models representing thepatient's teeth can be predicted using the digital models of the twopatient's teeth, in step 160. First buffer widths are calculated foreach digital tooth model. As shown in FIG. 17 , a coordinate system 1700comprising x, y, and z axes is established for a digital tooth model1710. Along the z direction, as shown in FIG. 17 , a plurality of lines1720 parallel to the z-axis are specified, typically at constantintervals. The lines 1720 intersect with the surfaces of the digitaltooth model 1710. The distance between the intersection points, of thesegment width, of each line 1720 is called buffer width. The bufferwidths are calculated along each of the x, y, and z directions.

An orthogonal bounding box 1800 can be set up as shown in FIG. 18 toassist the calculation of the buffer widths. The bounding box definesmaximum range for the digital tooth model along each direction in thecoordinate system 1810. The bounding box 1800 includes three pairs ofrectangle faces in three directions. To calculate the buffer width alongthe z direction, a grid of fixed intervals is set up over therectangular x-y face 1820 of the bounding box 1800.

The intervals of the grid 1900 along x and y direction, shown in FIG. 19, are defined in accordance with the precision requirement. The gridnodes define start and end points for the lines 1720. The grid nodes areindexed. The segment width (i.e., the buffer width) is calculated foreach pair of indexed grid nodes at the two opposite rectangular faces othe bounding box 1800. The buffer widths can be resealed and stored forexample in 8 bit or 16 bit values.

The interference between two physical tooth models to be fabricatedbased on the digital tooth models can be predicted using thecorresponding digital tooth models. As shown in FIG. 20 , the twodigital tooth models 2010 and 2020 overlap in the overlapping portion2030. The buffer widths of each of the digital tooth models 2010 and2020 are translated into a common coordinate system. For each of theline 1720, intersection points for each of the digital tooth models 2010and 2020 are determined or retrieved. The interference depth or thedepth of overlapping portion 2030 can be calculated along the line inthe z direction. The calculation of the interference depth is repeatedfor each pair of the x-y grid nodes similar to the procedure describedabove for each digital tooth model. The maximum interference depth canbe determined among all the interference depths between the two digitaltooth models.

The simulation of the interference between digital tooth models servesas prediction of the interference between the physical tooth modelsafter they are fabricated and assembled to form a physical dental basemode. The knowledge of the interference between the physical toothmodels can be used to prevent such interference to occur. One way toprevent such interference is by adjusting features affixed to thephysical tooth models. Another method to prevent the interference is theadjust teeth positions in a dental arch model. Both methods are valuableto an orthodontic treatment.

The tooth models can be affixed with one or more pins at their bottomportions for the tooth models to be inserted into the base. The twoadjacent tooth models can interfere with each other when they areinserted into a base. The pin configurations are selected in step 170 toprevent interference between adjacent tooth models.

Two adjacent tooth models 1010 and 1020 are shown in FIGS. 10 . Thetooth models 1010, 1020 are respectively affixed with pins 1015 and pins1025. The orthodontic treatment requires the two adjacent tooth models1010 and 1020 to be tilted away from each other in a tooth arch model.As a result, the pins 1015 and the pins 1025 interfere with or collideinto each other. In another example, as shown in FIG. 11 , two adjacenttooth models 1110 and 1120 are required to tilt toward each other by theorthodontic treatment. The tooth models 1110 and 1120 are affixed withpins having equal pin lengths. The tooth models 1110 and 1120 cancollide into each other when they are inserted into a base 1130 becausethe insertion angles required by the long insertion pins.

In accordance with the present invention, the interference betweenadjacent tooth models mounted on an arch can be resolved by properlydesigning and selecting configurations of the pins affixed to the bottomportion of the tooth models. FIG. 12 illustrates a tooth model 1200having two pins 1210 and 1220 affixed to the bottom portion. To preventinterference of the tooth model 1200 with its neighboring tooth models,the pins 1210 and 1220 are designed to have different lengths.

FIGS. 13(a) and 13(b) show detailed perspective views how two toothmodels having the pin configurations shown in FIG. 12 can avoidinterfering with each other. FIG. 13(a) shows the front perspective viewof two tooth models 1310 and 1320 each of which is respectively affixedpins 1315 and 1325. The pins 1315 and pins 1325 are configured to havedifferent lengths so that the pins do not run into each other when theyare inserted into a base (not shown in FIG. 13(a) for clarity). Theavoidance of interference between the tooth models 1310 and 1320 is alsoillustrated in a perspective bottom view in FIG. 13(b).

The pin configurations for tooth models can be selected by differentmethods. In one embodiment, a digital dental arch model that representsthe physical tooth model is first produced or received. The digitaldental arch model defines the positions and orientations of the twoadjacent physical tooth models in the physical dental arch modelaccording to the requirement of the orthodontic treatment. The positionsof the physical tooth models including the pins are simulated to examinethe interference between two adjacent physical tooth models mounted onthe base. The pin configurations are adjusted to avoid any interferencethat might occur in the simulation. The pin configurations can includepins lengths, pin positions at the underside of the tooth models, andthe number of pins for each tooth model.

The tooth models affixed with pins having the selected pinconfigurations can fabricated by Computer Numerical Control (CNC) basedmanufacturing in response to the digital dental arch model. At differentsteps of an orthodontic treatment, the tooth portions of the toothmodels can remain the same while the pins affixed to the tooth portionbeing adjusted depending on the relative orientation of positionsbetween adjacent tooth models. Furthermore, the base can includedifferent socket configurations adapted to receive compatible pinconfigurations selected for different steps of the orthodontictreatment. The physical tooth models and their pin configurations can belabeled by a predetermined sequence to define the positions of thephysical tooth models on the base for each step of the orthodontictreatment.

An advantage of the present invention is that the different pinconfigurations allow longer pins affixed to the tooth models, whichresults in more stable physical tooth arch model. Another advantage isthat the tooth portion of the tooth models can be reused for differentsteps of an orthodontic treatment. Modular sockets can be prepared onthe underside of the tooth models. Pins of different lengths can beplugged into the sockets to prevent interference between adjacent toothmodels.

Before casting the arch from the impression, the base plate is takenthrough a CNC process to create the female structures for eachindividual tooth (step 180). Then the base is placed over the castingcontainer in which the impression is already present, and the containeris filled with epoxy. The epoxy gets filled up in the female structuresand the resulting mold has the male studs present with each tooth modelthat can be separated afterwards. FIG. 2 shows a tooth model 210 withmale stud 220 after mold separation. The base 230 comprises a femalefeature 240 that can receive the male stud 220 when the tooth model 210is assembled to the base 230.

Alternatively, as shown in FIG. 3 , a tooth model 310 includes a femalesocket 315 that can be drilled by CNC based machining after casting andseparation. A male stud 320 that fits the female socket 315 can beattached to the tooth model 310 by for example, screwing, glueapplication, etc. The resulted tooth model 330 includes male stud 310that allows it to be attached to the base.

Male protrusion features over the tooth model can exist in a number ofarrangements. FIG. 4 shows a tooth model 410 having two pins 415sticking out and a base 420 having registration slots 425 adapted toreceive the two pins 415 to allow the tooth model 410 to be attached tothe base 420. FIG. 5 shows a tooth model 510 having one pins 515protruding out and a base 520 having a hole 525 adapted to receive thepin 515 to allow the tooth model 510 to be attached to the base 520. Ingeneral, the tooth model can include two or more pins wherein the basewill have complementary number of holes at the corresponding locationsfor each tooth model. The tooth model 610 can also include cone shapedstuds 620 as shown in FIG. 6 . The studs can also take a combination ofconfigurations described above.

As shown FIG. 7 , the studs protruding out of the tooth model 710 cantake different shapes 720 such as oval, rectangle, square, triangle,circle, semi-circle, each of which correspond to slots on the basehaving identical shapes that can be drilled using the CNC basedmachining. The asymmetrically shaped studs can help to define a uniqueorientation for the tooth model on the base.

FIG. 8A shows a base 800 having a plurality of sockets 810 and 820 forreceiving the studs of a plurality of tooth models. The positions of thesockets 810, 820 are determined by either her initial teeth positions ina patient's arch or the teeth positions during the orthodontic treatmentprocess. The base 800 can be in the form of a plate as shown in FIG. 8 ,comprising a plurality of pairs of sockets 810, 820. Each pair ofsockets 810, 820 is adapted to receive two pins associated with aphysical tooth model. Each pair of sockets includes a socket 810 on theinside of the tooth arch model and a socket 820 on the outside of thetooth arch model.

Another of a base 850 is shown in FIG. 8B. A plurality of pairs offemale sockets 860, 870 are provided in the base 850. Each pair of thesockets 860, 870 is formed in a surface 880 and is adapted to receive aphysical tooth model 890. The bottom portion of the physical tooth model890 includes a surface 895. The surface 895 comes to contact with thesurface 880 when the physical tooth model 890 is inserted into the base850, which assures the stability of the physical tooth model 890 overthe base 850.

A tooth model 900 compatible with the base 800 is shown in FIG. 9 . Thetooth model 900 includes two pins 910 connected to its bottom portion.The two pins 910 can be plugged into a pair of sockets 810 and 820 onthe base 800. Thus, each pair of sockets 810 and 820 uniquely definesthe positions of a tooth model. The orientation of the tooth model isalso uniquely defined if the two pins are labeled as inside and outside,or the sockets and the pins are made asymmetric inside and outside. Ingeneral, each tooth model may include correspond to one or a pluralityof studs that are to be plugged into the corresponding number ofsockets. The male studs and the sockets may also take different shapesas described above.

In another embodiment, the disclosed methods and system can includeteeth duplicate with removable or retractable pins, as shown in FIGS. 14and 15 . A tooth model 1450 is placed on a flat surface 1460 in a recesscreated in the base 1440. The base 1440 include through holes 1425 and1435. The tooth model 1450 includes at the bottom portion drilled holes1420 and 1430 that are in registration and alignment with the throughholes 1425 and 1435. Pins 1410 can then be inserted along directions1412, 1413 into the through holes 1425 and 1435 in the base and thenholes 1420 and 1430 in the base to affix the tooth models 1450 into thebase 1440.

In another embodiment, the tooth model 1510 includes holes 1520. Pins1540 and 1550 can be inserted into the holes 1520 in spring loadmechanisms 1530, 1540. The pins 1540 are retractable with compressedsprings to avoid interference during insertion or after the installationof the tooth model over the base. After the tooth models are properlymounted and fixed, the pins 1540 can extend to their normal positions tomaximize position and angle control. The overall pin lengths can be cutto the correct lengths to be compatible with the spring load mechanismsto prevent interference between tooth models.

The described methods are also applicable to prevent tooth modelinterference in precision mount of tooth models in casting chambers. Insuch cases, the shape and the height of the tooth models can be modifiedto avoid interference of teeth during insertion or at the correspondingtreatment positions.

A tooth arch model is obtained after the tooth models are assembled tothe base 800 (step 190). The base 800 can comprise a plurality ofconfigurations in the female sockets 810. Each of the configurations isadapted to receive the same physical tooth models to form a differentarrangement of at least a portion of a tooth arch model.

The base 800 can be fabricated by a system that includes a computerdevice adapted to store digital tooth models representing the physicaltooth models. As described above, the digital tooth model can beobtained by various scanning techniques. A computer processor can thengenerate a digital base model compatible with the digital tooth models.An apparatus fabricates the base using CNC based manufacturing inaccordance with the digital base model. The base fabricated is adaptedto receive the physical tooth models.

The physical tooth models can be labeled by a predetermined sequencethat defines the positions of the physical tooth models on the base 800.The labels can include a barcode, a printed symbol, hand-written symbol,a Radio Frequency Identification (RFID). The female sockets 810 can alsobe labeled by the parallel sequence for the physical tooth models.

In one embodiment, tooth models can be separated and repaired after thebase. The tooth models can be removed, repaired or replaced, andre-assembled without the replacement of the whole arch model.

Common materials for the tooth models include polymers, urethane, epoxy,plastics, plaster, stone, clay, acrylic, metals, wood, paper, ceramics,and porcelain. The base can comprise a material such as polymers,urethane, epoxy, plastics, plaster, stone, clay, acrylic, metals, wood,paper, ceramics, porcelain, glass, and concrete.

The arch model can be used in different dental applications such asdental crown, dental bridge, aligner fabrication, biometrics, and teethwhitening. For aligner fabrication, for example, each stage of the teethtreatment may correspond a unique physical dental arch model. Alignerscan be fabricated using different physical dental arch models one at atime as the teeth movement progresses during the treatment. At eachstage of the treatment, the desirable teeth positions for the next stageare calculated. A physical dental arch model having modified teethpositions is fabricated using the process described above. A new aligneris made using the new physical dental arch model.

In accordance with the present invention, each base is specific to anarch configuration. There is no need for complex and costly mechanismssuch as micro-actuators for adjusting multiple degrees of freedom foreach tooth model. The described methods and system is simple to make andeasy to use.

The described methods and system are also economic. Different stages ofthe arch model can share the same tooth models. The positions for thetooth models at each stage of the orthodontic treatment can be modeledusing orthodontic treatment software. Each stage of the arch model mayuse a separate base. Or alternatively, one base can be used in aplurality of stages of the arch models. The base may include a pluralityof sets of receptive positions for the tooth models. Each setcorresponds to one treatment stage. The tooth models can be reusedthrough the treatment process. Much of the cost of making multiple tootharch models in orthodontic treatment are therefore eliminated.

Although specific embodiments of the present invention have beenillustrated in the accompanying drawings and described in the foregoingdetailed description, it will be understood that the invention is notlimited to the particular embodiments described herein, but is capableof numerous rearrangements, modifications, and substitutions withoutdeparting from the scope of the invention. The following claims areintended to encompass all such modifications.

1-2. (canceled)
 3. A method for preventing interference between twophysical tooth models coupled to a base about one or more pins so as toform a physical model of an arrangement of teeth, the method comprising:generating digital representations of two physical tooth models;receiving position data of the digital representations of the twophysical tooth models; predicting the interference of the two physicaltooth models based at least in part on the position data; and selectingan adjusted pin configuration for a physical model of an arrangement ofteeth so as to avoid the predicted interference.
 4. The method of claim3, wherein the wherein the digital representations of the two physicaltooth models intersect to form an overlapping portion according to theposition data.
 5. The method of claim 4, wherein predicting theinterference of the two physical tooth models is based at least in parton the overlapping portion between the digital representations.
 6. Themethod of claim 3, further comprising acquiring coordinates of aplurality of points on the surfaces of the two physical tooth models. 7.The method of claim 6, wherein said acquiring comprises measuring thepositions of points on the surfaces of an impression representing apatient's teeth.
 8. The method of claim 3, wherein generating saidrepresentations comprises generating digital meshes of points in threedimensions, wherein the meshes represent the surfaces of the twophysical tooth models.
 9. The method of claim 8, wherein the meshes aregenerated using coordinates of a plurality of points on the surfaces ofthe two physical tooth models.
 10. The method of claim 8, wherein themeshes are triangular meshes in three dimensions.
 11. The method ofclaim 8, wherein at least one of the meshes comprises at least one meshopening having three, four or five nodes.
 12. The method of claim 3,further comprising making an adjustment to eliminate the interferencewhen the two physical tooth models are mounted to a base.
 13. The methodof claim 12, wherein said making comprises adjusting the position ororientation of at least one of the two physical tooth models.
 14. Themethod of claim 12, wherein said making comprises selectingconfigurations of first features of the two physical tooth models. 15.The method of claim 14, further comprising fabricating the physicaltooth models having the selected configurations of first features. 16.The method of claim 14, wherein the configurations of first features areselected in accordance with a depth of the overlapping portion betweenthe two physical tooth models.
 17. The method of claim 12, wherein saidmaking comprises selecting the positions and orientations of secondfeatures on a base to prevent interference between the two physicaltooth models when they are mounted to the base with the assistance ofthe second features.
 18. The method of claim 17, further comprisingfabricating the base having the selected positions and orientations ofthe second features.
 19. The method of claim 12, wherein said makingcomprises digitally adjusting at least one of the digitalrepresentations.
 20. The method of claim 19, further comprisingadjusting the position or orientation of at least one of the twophysical tooth models in accordance with the digital adjustment to theat least one of the digital representations.
 21. The method of claim 19,further comprising adjusting a configuration of at least one of thefirst features of the two physical tooth models in accordance with thedigital adjustment to the at least one of the digital representations.22. The method of claim 12, wherein said generating comprisescalculating a depth of the overlapping portion between the digitalrepresentations, and wherein said making comprises adjusting theposition or orientation of at least one the two physical tooth models inaccordance with the calculated depth to prevent the interference betweenthe two physical tooth models.